Robust Control Performance for Open Quantum Systems

• 成果类型: Article
• 署名作者: Schirmer, Sophie G.; Langbein, Frank C.; Weidner, Carrie Ann; Jonckheere, Edmond
• 署名单位: Swansea University; Cardiff University; University of Bristol; University of Southern California
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3181249
• 发表日期: 2022
• 页码: 6012-6024
• 关键词: H-infinity control; quantum information and control; Robust control; uncertain systems

摘要

Robust performance of control schemes for open quantum systems is investigated under classical uncertainties in the generators of the dynamics and non-classical uncertainties due to decoherence and initial state preparation errors. A formalism is developed to measure performance based on the transmission of a dynamic perturbation or initial state preparation error to the quantum state error. This makes it possible to apply tools from classical robust control, such as structured singular value analysis. A difficulty arising from the singularity of the closed-loop Bloch equations for the quantum state is overcome by introducing the #-inversion lemma, a specialized version of the matrix inversion lemma. Under some conditions, this guarantees continuity of the structured singular value at s = 0. Additional difficulties occur when symmetry gives rise to multiple open-loop poles, which under symmetry-breaking unfold into single eigenvalues. The concepts are applied to systems subject to pure decoherence and a general dissipative system example of two qubits in a leaky cavity under laser driving fields and spontaneous emission. A nonclassical performance index, steady-state entanglement quantified by the concurrence, a nonlinear function of the system state, is introduced. Simulations confirm a conflict between entanglement, its log-sensitivity and stability margin under decoherence.